Question: Simplify the following expression: $\dfrac{48x^5}{24x}$ You can assume $x \neq 0$.
Answer: $ \dfrac{48x^5}{24x} = \dfrac{48}{24} \cdot \dfrac{x^5}{x} $ To simplify $\frac{48}{24}$ , find the greatest common factor (GCD) of $48$ and $24$ $48 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $24 = 2 \cdot 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(48, 24) = 2 \cdot 2 \cdot 2 \cdot 3 = 24 $ $ \dfrac{48}{24} \cdot \dfrac{x^5}{x} = \dfrac{24 \cdot 2}{24 \cdot 1} \cdot \dfrac{x^5}{x} $ $\phantom{ \dfrac{48}{24} \cdot \dfrac{5}{1}} = 2 \cdot \dfrac{x^5}{x} $ $ \dfrac{x^5}{x} = \dfrac{x \cdot x \cdot x \cdot x \cdot x}{x} = x^4 $ $ 2 \cdot x^4 = 2x^4 $